One word request - Synonymous with noun "shreds" and connotative of squishy bits?

Solution 1:

Gobbet might work as an evocative alternative. ODO defines it as "A piece or lump of flesh, food, or other matter". Unfortunately, it doesn't carry the same shape connotations as shred...

Solution 2:

This might or might not be useful to you, because it's pretty informal, but sometimes when people talk about video games, a character being damaged and exploding into lots of bloody lumps of flesh as a result is called being "gibbed". The bits themselves are called "gibs", which comes from "giblet". Giblets are the edible internal stuff that's in a fowl.

Not sure if you would want to use the word "giblets" in the context you gave, but it is a noun that makes me think of scraps of flesh.